YES(?,O(n^1))

Problem:
 f(a(),x) -> g(a(),x)
 g(a(),x) -> f(b(),x)
 f(a(),x) -> f(b(),x)

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5}
   transitions:
    f1(8,5) -> 5*
    b1() -> 8*
    g1(7,5) -> 5*
    a1() -> 7*
    f2(9,5) -> 5*
    f0(5,5) -> 5*
    b2() -> 9*
    a0() -> 5*
    g0(5,5) -> 5*
    b0() -> 5*
  problem:
   
  Qed